Demonstration of Raman–Ramsey fringes using time delayed optical pulses G.S. Pati

Optics Communications 281 (2008) 4676–4680
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Optics Communications
journal homepage: www.elsevier.com/locate/optcom
Demonstration of Raman–Ramsey fringes using time delayed optical pulses
in rubidium vapor
G.S. Pati a,c,*, K. Salit a, Renu Tripathi b, M.S. Shahriar a
a
Department of EECS, Northwestern University, 2145 N. Sheridan Road, Evanston, IL 60208, United States
Palomar Observatory, California Institute of Technology, Pasadena, CA-91125, United States
c
Department of Physics & Pre-Engineering, Delaware State University, Dover, DE-19901, United States
b
a r t i c l e
i n f o
Article history:
Received 14 August 2007
Received in revised form 16 April 2008
Accepted 27 May 2008
OCIS Codes:
020.1670
020.3690
300.6450
a b s t r a c t
We report observation of high contrast Raman–Ramsey fringes using time delayed optical pulse pairs in a
rubidium vapor cell. The width of these fringes are not limited by saturation and provides a simpler
means to produce narrow atomic linewidths using a thermal vapor medium for compact atomic clock
applications. We also demonstrate phase-scanned Raman–Ramsey fringes, with potential application
to sensitive detection of trace vapors.
Ó 2008 Published by Elsevier B.V.
For many applications, there is a need to develop a very compact atomic clock with high accuracy. For example, such a clock
could be built into next-generation GPS (Global Positioning System) receivers in order to enhance the navigation accuracy. The
conventional approach for an atomic clock employs the excitation
of hyperfine resonances in alkali atoms such as Cs or Rb using
microwave fields enhanced by a cavity. The size of such a cavity
represents a fundamental limitation to the volume and the weight
of the clock. However, this problem can be circumvented by exciting the same resonance indirectly, using a two-photon, resonantRaman transition that corresponds to the effect popularly known
as Coherent Population Trapping (CPT) [1]. The CPT based atomic
clock was first demonstrated by the group of Shaoul Ezekiel at
MIT, using a dye laser, bulk acousto-optic modulators, and a sodium atomic beam [2–4]. These experiments report observations
of Ramsey fringes by using resonant Raman transitions in two separated regions of an atomic beam. Small, transit-time limited linewidths are obtained using a large separation (upto 30 cm) between
the exciting zones. Subsequently, a directly modulated semiconductor laser was used by the same group to demonstrate the CPT
clock using a Cs atomic beam [5]. A clear, quantitative analysis of
the improvement in contrast obtained by optical Ramsey fringes
in various traveling-wave interaction geometries can be found in
an early paper by Borde et al. [6]. Since then, significant develop-
* Corresponding author. Current address: Department of Physics & Pre-Engineering, Delaware State University, Dover, DE-19901, United States. Tel.: +1 847 491
7308; fax: +1 847 491 4455.
E-mail address: [email protected] (G.S. Pati).
0030-4018/$ - see front matter Ó 2008 Published by Elsevier B.V.
doi:10.1016/j.optcom.2008.05.056
ments have taken place in making the CPT clock more compact
and robust [7,8].
Of particular significance in this development is the use of vapor
cells to replace atomic beams. In order to overcome the transit
time induced broadening of the CPT resonance, these cells are typically loaded with a buffer gas, leading to sub-kHz linewidths.
However, there remains a key difference with the atomic beam
(AB) based approach, which limits the accuracy of the vapor-CPT
clocks. In the AB approach, the atoms interact with the optical
fields in two separate zones, which is the Raman version of
Ramsey’s separated fields excitation scheme [9]. The resulting Raman–Ramsey fringe pattern has a linewidth determined primarily
by the time-separation between the two zones. The advantages of
this approach are as follows. First, the CPT process can be saturated
in the first interaction zone in order to maximize the signal amplitude, without power-broadening the Raman–Ramsey fringes. Second, the saturation in the first zone also suppresses the process
of shifting the clock transition frequency due to the AC Stark effect
[4]. In contrast, the vapor-CPT approach uses a single-zone excitation, so that the linewidth of the CPT signal is limited by powerbroadening, and the AC Stark effect is not suppressed effectively.
These problems can be circumvented by using a pair of time-delayed optical pulses in order to produce Raman–Ramsey fringes in
a vapor cell. Here, we report on the observation of such fringes
using a rubidium vapor cell. In our experiment, Raman transition
is produced between the long-lived hyperfine ground states of
the D2 line in 85Rb vapor. An earlier experiment by Salour and Cohen-Tannoudji [10] explored a similar approach using short optical
pulses (nanosecond) and rapidly decaying atomic states (lifetime
G.S. Pati et al. / Optics Communications 281 (2008) 4676–4680
5 108 s) of sodium for high-resolution spectroscopy application.
This involved practical difficulties in generating time-delayed,
phased-locked short pulses from the laser amplifiers. In contrast,
the Ramsey excitation reported here is carried out using long optical pulses, since it involves a Raman transition between long-lived
metastable ground states. A theoretical proposal by Dubetsky et al.
[11] considered generating stimulated echo and Ramsey fringes
sensitive to small changes in atomic velocity by using a sequential
excitation of atoms by two counterpropagating traveling waves. A
recent experiment [12] has reported a similar approach for observing high contrast fringes in thermal Cs vapor using delayed pulses,
using a double-lambda scheme. Such a scheme requires a four-level system, which in this case is created using Zeeman sublevels of
the same hyperfine excited level. In our scheme, a simple three-level K-type scheme has been shown to produce high-contrast
fringes both by changing the Raman detuning as well as by
scanning the phase of the interrogating pulse without perturbing
the dark state. The phase scan technique can be used in sensing
applications where, for example, the interrogating pulse can be
sent through a trace medium for determining the trace
concentration.
Ramsey fringes are observed experimentally in the amplitude of
the time-delayed second probe pulse by varying the frequency
detuning between the pump and the probe away from resonant
Raman excitation. An electronic time-gated measurement has been
used to observe the amplitude oscillation of the second pulse. The
width of observed Ramsey fringes is limited only by the inverse of
the time delay between the pulse pairs. In practice, this width can
be made very small compared to the resonance linewidth observed
during continuous excitation, if the medium dephasing time can be
made long either by using buffer gas [13] or by using wall coating
[14] to preserve the coherence. We also used an alternative approach to Raman–Ramsey oscillations by independently scanning
the phase of the second probe pulse with respect to the first pulse
using a piezo-actuated mirror, while keeping the difference frequency matched close to the two photon resonance condition. In
all these experiments, no special care (such as adding buffer gas
or paraffin coating) is taken to prevent rapid medium decoherence,
which leaves room for significant improvements.
The inset in Fig. 1 shows a three level K-scheme used in the D2
line of 85Rb using two coherent laser fields, x1 and x2. In the
experiment, states 5S1/2 (F = 2) and 5S1/2 (F = 3) are used as two
long-lived ground states and the hyperfine excited state 5P3/2
(F = 3) is used as the excited upper level for the K-system. Coherent Raman excitation using the resonant optical fields on the two
atomic transitions produces a dark superposition state [15],
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ji ¼ ½X2 j1i X1 j2i= X21 þ X22 , where X1, X2 are the Rabi frequencies associated with the Raman fields, that exhibits CPT in
such a K-system. When the atom is put in this particular superposition state, it remains in the dark state, which is uncoupled from
the excited state. As a result, the medium appears transparent after
the dark state is established. In our experiment, the linewidth of
the CPT resonance is observed in continuous excitation by sweeping the two-photon (or difference) detuning d between the two
(pump and probe) laser fields. For the copropagating fields in the
vapor medium, the resonant two-photon linewidth is unaffected
by the Doppler broadening, and is determined by other sources
such as light intensities, transit time of atoms and the decay rate
between ground states. In experiments using the continuous excitation, the linewidth of resonance is primarily governed by the saturation caused due to light intensities.
The contrast of the resonant signal is determined by the fraction
of total number of atoms trapped in the dark state. If orthogonal,
circular polarizations are used for the pump and the probe, a large
fraction of atomic population get trapped in Zeeman sublevels due
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to optical pumping caused by laser fields via resonant and off-resonant excitations. This causes significant reduction in the contrast
of the CPT signal. In order to circumvent this problem, we have
used orthogonal, linear polarizations for the pump and the probe
beams [12,16,17], as discussed further later on.
Fig. 1a shows the schematic of our experimental setup used in
both continuous and pulsed Raman excitations. A frequency stabilized Ti: Sapphire laser is used to produce resonant laser fields at
frequencies x1 and x2. These are obtained by using acousto-optic
modulators (AOMs) driven by microwave voltage controlled oscillators (VCOs). For the two photon Raman resonance, the frequency
difference between x1 and x2 is matched to the ground state splitting (3.0357 GHz) of 85Rb. Fig. 1c shows the energy diagram used
for the CPT excitation in Rb85 atoms. This is achieved by using
two high frequency AOMs made by the Brimrose corporation (center frequency (fo) = 1.5178 GHz. bandwidth (Df) = 200 MHz, diffraction efficiency 25%) in the paths of the probe and pump
beams, the probe frequency being upshifted and the pump frequency being downshifted from the laser frequency. The orthogonally polarized beams are combined using a polarizing beam
splitter. They are sent through a piece of polarization maintaining
optical fiber in order to produce a good spatial mode. The use of the
optical fiber also ensures perfect co-propagation between the
pump and the probe. This is particularly important for observing
very narrow Raman–Ramsey fringes [18]. The beams are expanded
and collimated to about 5 mm (1/e2 diameter) before sending them
through a 10 cm long rubidium vapor cell. The vapor cell is
magnetically shielded using a l-metal box and wrapped with
twisted coils to minimize the effect of magnetic field produced
due to heating. Raman excitation using the orthogonal, linear
polarizations creates dark states as a superposition of the
jF ¼ 2; mF ¼ 0i ; jF ¼ 3; mF ¼ 0i levels of the ground states for
both the r+ and r components of the linearly polarized beams.
This is because the ratios of Clebsch–Gordan coefficients for r
polarizations are equal and opposite for the D2 transitions:
jDarkir ¼ jDarkirþ for ½X1 =X2 rþ ¼ ½X1 =X2 r . Experimentally
CPT resonance of linewidth as narrow as 400 KHz has been observed for the probe power 0.25 mW and a pump four times
stronger than the probe.
To observe Raman–Ramsey fringes, we used a repeated sequence of time-delayed optical pulse pairs in the vapor medium.
These optical pulses are generated by sending Rf pulses from a
pulse generator to the high-frequency AOMs. Both the pump and
the probe beams are pulsed simultaneously using the independent
AOMs shown in Fig. 1a. During the observation of the probe transmission, the pump pulse is filtered out using a polarizer. The duration N1 of the first pulse is chosen to be sufficiently long in order to
cause efficient excitation of atoms into the dark state. The atoms
are then probed using a second pulse of duration N2. The second
pulse is kept short and relatively weak, in order not to perturb significantly the dark state produced by the longer and stronger first
pulse. In the experiment, N1 and N2 are chosen to be 500 ns and
100 ns, respectively. The fringes are observed in the transmitted
amplitude of the second pulse by slowly varying the difference frequency d while using a repeated sequence of pulses. The probe
amplitude of the second pulse is measured using a gated integrator
and boxcar averager.
The conceptual diagram in Fig. 2a1 shows repeated pulse pairs
during a slow d-scan that spans the single-zone CPT line-width.
After each coherent excitation by the first (blue) pulse, the atoms
are driven into the dark state and are interrogated by the second
(red) pulse. The amplitude of the second probe pulse oscillates as
1
For interpretation to color in Fig. 2, the reader is referred to the web version of
this article.
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G.S. Pati et al. / Optics Communications 281 (2008) 4676–4680
Shielded Rb
vapor cell
Polarizer
Optical
fiber
Detector
Gated Integrator &
Boxcar Averager
G
AOM1
fo = 1..5178 MHz
Probe
Oscilloscope
VCO
AOM2
fo = -1.5178 MHz
VCO
a
Pump
PZT
z
3
Probe 1
Pump
Probe pulses
Probe
AOM
fo = 80 MHz
2
d
AOM
fo = 80 MHz
Probe 2
b
3.0357 GHz
1
c
Fig. 1. (a) Layout of the experimental arrangement, fo corresponds to the center frequency of the AOMs. While observing the CPT signal, a probe power of 250 lW and a pump
power 1 mW have been used. (b) Experimental scheme used to generate independent phase scan of the second probe pulse. (c) Energy diagram for the CPT excitation in
rubidium (85Rb D2 line) vapor.
a function of d as shown in Fig. 2b, giving rise to the Raman–Ramsey oscillations [19]. The Raman–Ramsey oscillations occur as long
as the delay T between the pulse pair is smaller than the medium
dephasing time. The dephasing time between the ground states in
our experiment is measured to be approximately few microseconds, primarily limited due to collision (atom–atom and atom–
wall) induced dephasing. However, the relaxation can be improved
significantly by adding inert buffer gases [14].
In the experiment, the delayed pulse pairs are repeated after
every 100 ls interval. While sending repeated pulse pairs, the difference frequency d between the probe and pump frequencies is
scanned over a range of 4 MHz around the two photon resonance
(d = 0, which corresponds to x1 x2 = 3.0357 GHz) at a slow rate
of 10 Hz. This allows us to sample the Raman–Ramsey oscillations
with nearly 1000 pulses using the gated boxcar averager. The integration mode in the boxcar also allows us to observe extremely
small amplitude oscillations in the second pulse. Fig. 3a and b
shows experimentally observed Ramsey fringes using different
time-delays T between the first and second optical pulse. The
traces in red color indicate the fringes observed in the amplitude
of the second probe pulse, whereas the ones in blue show the
corresponding amplitude variation of the first probe pulse. The
amplitude variation of the first pulse essentially corresponds to a
single-pulse, transit-time limited CPT resonance. The delay T for
evolution of the coherent dark state is varied in order to observe
the smallest width of the fringes. In our case, high contrast inter-
ference fringes are observed for delays upto 3 ls. The fringe width
at the center varies 1/2T, as expected, and is significantly narrower
than the CPT line-width. Away from the center, the amplitude of
oscillation decreases as the two photon resonance condition
(d = 0) is not exactly satisfied.
In an alternative approach, we used a phase scan technique instead of the d-scan to observe the Raman–Ramsey fringes. This is
done by slowly (at a rate of 10 Hz) and continuously scanning
the phase of the beat-note between the pump and the probe in
the second pulse with respect to the first pulse during the repeated
pulse sequence. For this purpose, two additional AOMs (with same
frequency shifts, 80 MHz) are used (Fig. 1b) in the probe beam to
generate independently the two delayed probe pulses. The diffracted beams from both these AOMs are then combined, before
they are sent through a common AOM (1.4378 GHz). Using a
piezo-actuated mirror (PM) in one of the AOM beam paths allows
us to continuously scan the phase of the second pulse (generated
by that AOM) using a voltage ramp. Fig. 3c shows the Ramsey oscillations observed in the amplitude of the second pulse when the difference frequency between the pump and probe is set close to the
two photon resonance peak, i.e., d = 0. The number of oscillations
corresponds to the phase cycle of the second pulse, which in our
case is limited by the motion of the piezo-actuator. The phase U
as a function of the scan time t is given by ðx1 =c Þdmax fscan t, where
dmax is the maximum translation of the actuator and fscan is the rate
of scan. Fig. 3c shows oscillations for two different time separa-
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G.S. Pati et al. / Optics Communications 281 (2008) 4676–4680
a
Strong pump-probe
2γ
Weak pump-probe
δ
0
time
1st pulse
τ1 = 500 ns
-2γ
b
pulse delay
T
2nd pulse
τ2 = 100 ns
pulse pair repeat sequence
τr = 100 μs
t = to , Δ = 0
Oscillation in 1st pulse
δ.τd = 1
Raman Ramsey
oscillation 2nd pulse
Fig. 2. Illustrative diagrams showing (a) the repeated pulse sequence, where the straight line ramp represents a gradual scan of the pump and probe difference frequency
around the two-photon resonance condition (d = 0), and (b) Raman–Ramsey oscillations in the second pulse amplitude.
Fig. 3. Experimentally observed Raman–Ramsey oscillations with time delays (a) T = 1.8 ls (b) 2.2 ls. The blue trace indicates the amplitude of the first pulse and the red
indicates the Ramsey oscillations in amplitude of the second pulse. The width of the central fringe in (a) 280 KHz, (b) 230 KHz, (c) Ramsey oscillations observed using the
phase scan for pulse time delays T = 1 ls and 1.5 ls. The dashed line correspond to the voltage ramp applied to the piezo-actuator to produce the phase scan at 10 Hz rate.
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G.S. Pati et al. / Optics Communications 281 (2008) 4676–4680
tions between the pulse pairs. The coherence produced by the first
pulse is preserved during the free time evolution, which is probed
by the second pulse that carries a different phase to produce the
Raman–Ramsey fringes. It is possible to phase lock these oscillations using a reference signal generated by a separate interferometer. This can yield a high signal to noise ratio for phase sensitive
detection, with possible application to detection of trace vapors.
The primary motivation for the results reported here is the
enhancement of the stability of a CPT-based Rb vapor clock. In order to demonstrate the actual enhancement achievable, it is necessary for us to use a buffer gas filled cell and preferably use a diode
laser for exciting the CPT transition. Efforts are currently underway
to perform such an experiment.
Acknowledgments
This work was supported in part by the Hewlett–Packard Co.
through DARPA and the Air Force Office of Scientific Research under AFOSR Contract No. FA9550-05-C-0017, and by AFOSR Grant
No. FA9550-04-1-0189.
References
[1] G. Alzetta, A. Gozzini, L. Moi, G. Orriols, Nuovo Cimento 36B, An experimental
method for the observation of rf transitions and laser beat resonances in
oriented Na vapor 5 (1976).
[2] J. Thomas, P.R. Hemmer, S. Ezekiel, C.C. Leiby, R.H. Picard, C.R. Willis,
Observation of Ramsey fringes using a stimulated Resonance Raman
Transition in a sodium Atomic Beam, Phys. Rev. Lett. 48 (1982) 867.
[3] P.R. Hemmer, G.P. Ontai, S. Ezekiel, Precision studies of stimulated-resonance
Raman interactions in an atomic beam, J. Opt. Soc. Am. B3 (1986) 219.
[4] P.R. Hemmer, M.S. Shahriar, V.D. Natoli, S. Ezekiel, AC Stark shifts in a two-zone
Raman interaction, J. Opt. Soc. Am. B6 (1989) 1519.
[5] P.R. Hemmer, M.S. Shahriar, H. Lamela-Rivera, S.P. Smith, B.E. Bernacki, S.
Ezekiel, Semiconductor laser excitation of Ramsey fringes using a Raman
transition in a cesium atomic beam, J. Opt. Soc. Am. B10 (1993) 1326.
[6] C.J. Borde, C. Salomon, S. Avrillier, A.V. Lerberghe, C. Breant, D. Bassi, G. Scoles,
Optical Ramsey fringes with traveling waves, Phy. Rev. A 30 (1984) 1837.
[7] J. Vanier, M.W. Levine, D. Janssen, M.J. Delaney, Practical realization of a
passive coherent population trapping frequency standard, IEEE Trans. Inst.
Measur. 52 (2003) 258.
[8] M. Merimaa, T. Lindvall, I. Tittonen, E. Ikonen, All-optical atomic clock based on
coherent population trapping in Rb, J. Opt. Soc. Am. B20 (2003) 273.
[9] B.J. Dalton, T.D. Kieu, P.L. Knight, Theory of ultra-high-resolution Raman–
Ramsey spectroscopy, Opt. Acta 33 (1986) 459.
[10] M.M. Salour, C. Cohen-Tannoudji, Observation of Ramsey’s interference fringes
in the profile of doppler-free two-photon Resonances, Phys. Rev. Lett. 38
(1977) 757.
[11] B. Dubetsky, P.R. Berman, T. Sleator, Grating stimulated echo, Phys. Rev. A46
(1992) 2213.
[12] T. Zanon, S. Guerandel, E. de Clercq, D. Holleville, N. Dimarcq, A. Clairon, High
contrast Ramsey fringes with coherent-population-trapping pulses in a double
lambda atomic system, Phys. Rev. Lett. 94 (2005) 193002.
[13] E.E. Mikhailov, Y.V. Rostovtsev, G.R. Welch, Group velocity study in hot87Rb
vapour with buffer gas, J. Mod. Opt. 50 (2003) 2645.
[14] D. Budker, V. Yashchuk, M. Zolotorev, Nonlinear magneto-optics and reduced
group velocity of light in atomic vapor with slow ground state relaxation,
Phys. Rev. Lett. 81 (1998) 5788.
[15] E. Arimondo, Coherent population trapping in laser spectroscopy, Prog. Opt. 35
(1996) 259.
[16] F. Levi, A. Godone, J. Vanier, S. Micalizio, G. Modugno, Line-shape of dark line
and maser emission profile in CPT, Eur. Phys. J. D12 (2000) 53.
[17] M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, V.
Yudin, Coherent population trapping resonances in thermal85Rb vapor: D1
versus D2 line excitation, Opt. Lett. 27 (2002) 1462.
[18] If there is a small angle between the pump and the probe, it produces a
differential Doppler shift. This imposes a limit on the narrowest observable
fringes. In order to see a Raman–Ramsey fringe with a linewidth of cRR, the
maximum angle allowable between the pump and the probe is hmax 6 cRR =CD ,
where CD is the Doppler width of the vapor.
[19] M.S. Shahriar, P.R. Hemmer, D.P. Katz, A. Lee, M.G. Prentiss, Dark-state-based
three-element vector model for the stimulated Raman interaction, Phys. Rev.
A55 (1997) 2272.